Hecke duality relations of Jacobi forms

TL;DR

This paper introduces a new subspace of higher-degree Jacobi forms defined by Fourier coefficient relations, characterized by Hecke duality, and demonstrates its invariance under Hecke operators with explicit examples and counterexamples.

Contribution

It defines a novel subspace of Jacobi forms using Fourier coefficient relations and characterizes it via Hecke duality, establishing its invariance under all good Hecke operators.

Findings

The new subspace is Hecke invariant.

Explicit Eisenstein series are provided as examples.

Some forms do not belong to this subspace.

Abstract

In this paper we introduce a new subspace of Jacobi forms of higher degree via certain relations among Fourier coefficients. We prove that this space can also be characterized by duality properties of certain distinguished embedded Hecke operators. We then show that this space is Hecke invariant with respect to all good Hecke operators. As explicit examples we give Eisenstein series. Conversely we show the existence of forms that are not contained in this space.